In all recent applications, the basic building block of the EDF approach is the
Hartree-Fock-Bogoliubov (HFB) theory [1]}, which provides a
general method to determine an approximation of both the ground state and
excited states for a many-body quantum system described by a product-state wave
function. The HFB theory has been presented in great details in the review
articles [1]}, [3]}, [4]} as well as in several textbooks
[5]}, [6]}, [7]} and below we will only give a very brief
summary.
